Question

sin^2(x/2)=3cos^2(x/2)

Answer 1

$sin^2frac{x}{2}-3cos^2frac{x}{2}=0\\sin^2frac{x}{2}-3(1-sin^2frac{x}{2})=0\\4sin^2frac{x}{2}-3=0\\sin^2frac{x}{2}=frac{3}{4}\\frac{1-cosx}{2}=frac{3}{4}\\1-cosx=frac{3}{2}\\cosx=-frac{1}{2}\\x=pm(pi -frac{pi}{3})+2pi n,nin Z$

$x=pm frac{2pi }{3}+2pi n$